Perovskites
Perovskites are a class of compounds that have a similar crystal structure to the mineral perovskite (calcium titanate—CaTiO3). Like garnets and some other minerals, perovskites are network compounds—that is to say they are defined by a network of anions (negative ions, most commonly oxygen O2−) with specific holes for cations (positive ions, most commonly metallic elements). Half the metals in the periodic table can be inserted into the cation sites and still have a perovskite structure as long as constraints of valence and ionic size are met. The most common perovskite formula is ABO3, though other anions are possible and off-stoichiometry compounds with vacancies occur. The A site is a large 12-coordinated cubo-octahedral hole typically occupied by a cation with an ionic radius greater than or equal to that of O2− as this site is equivalent in size and coordination to an oxygen vacancy. The B site is a smaller 6-coordinated octahedral hole.
Ordered and disordered compounds with two cations on the A ((AzA′(1−z))BO3) or, more commonly, B (A(BxB′(1−x))O3) sites are possible with formula units and unit cells represented by multiples of the simple perovskite. Ordered and disordered A2BB′O6 (often written as A(B1/2B′1/2)O3) tends toward cubic/tetragonal/orthorhombic/monoclinic unit cells, while ordered A3BB′2O9 (often written as A(B1/3B′2/3)O3) tends toward hexagonal/rhombohedral unit cells.
The ABO3 stoichiometry constrains the sum of the average cation valences on the A and B sites of a stoichiometric oxide perovskite to be 6+, but that can be accomplished with various combinations. If the A site is populated completely by a divalent ion such as Pb2+, the average B site valence must be 4+. In particular A+2BxB′1−xO3 compounds occur in ordered and disordered states with stoichiometries that depend on the various B valences that must have a weighted average of 4+, e.g., A2+B3+1/2B′5+1/2O3 (½×3+½×5=4) and A2+B2+1/3B′5+2/3O3 (⅓×2+⅔×5=4).
Because of the common structure, solid solutions readily form between two perovskites, where two end members, e.g., ABO3 and A′B′O3 may mix with fractions 0<x<1 to a range of disordered materials AxA′1−xBxB′1−xO3. If A=A′ this is somewhat simplified to ABxB′1−xO3 as is the case for the materials discussed in this application. However, because solid solutions are not line compounds with a fixed composition, these have complex melting and crystallization behaviors as is well known to those familiar with the art. For even a simple binary solid solution phase diagram, the compound that crystallizes at any composition will tend to be biased toward the higher melting compound.
Perovskites comprise a number of technologically important materials because of their range of interesting properties. These materials can be ferroelectric, ferromagnetic, multiferroic, piezoelectric, pyroelectric, magnetic, magnetoresistive, electrooptic, magnetooptic, etc.
Piezoelectric Lead Zirconate Titanate
Lead zirconate titanate (PZT-Pb(ZrxTi1−x)O3) is a perovskite that is a solid solution between lead titanate (PT-PbTiO3) and lead zirconate (PZ—PbZrO3). It is piezoelectric, which is to say there is a linear electromechanical interaction between the mechanical and the electrical states of the material. The composition of most technological interest is nearly equimolar, Pb(Zr0.52Ti0.48)O3 at the morphotropic phase boundary (MPB) where the proximity of the rhombohedral-tetrahedral (R-T) phase transformation results in an increase in the dielectric permittivity and the piezoelectric coefficients. Additives are commonly used to tailor the piezoelectric, dielectric and particulate properties of piezoelectric PZT ceramics.
PZT is the most commonly used of the piezoelectric perovskites because of its excellent combination of piezoelectric and dielectric properties, high Curie temperature, high R-T transition temperature and ability to make both hard (high coercivity) and soft (low coercivity) materials. It is commercially available in ceramic form, though there are also experimental thin films formed by vapor phase methods. This is because, unlike some other piezoelectric perovskites, it has not successfully been grown as single crystals of any significant size. Both the PZ end member and all the PZT solid solutions are non-congruent, which is to say that this crystal composition cannot be grown from a melt of the same composition. Even the Bridgman method used successfully to grow non-congruent relaxor ferroelectric-PT solid solutions, as will be discussed below, cannot practically overcome the thermodynamic issues with this material. Therefore an invention is required to permit growth of single crystals of significant size.
The Pb(ZrxTi1−x)O3 room temperature lattice parameters near the MPB (x=0.52 atoms per formula unit (a/fu)) are given in Table I. The average of the a and b lattice parameters in the (001) plane is ˜4.055 Å at the MPB showing there is little dependence on the Zr concentration x. At high temperatures at which crystals might be grown, this compound becomes cubic in structure.
TABLE IPb(ZrxTi1−x)O3 lattice parameters in Å.x (a/fu)a (Å)b (Å)c (Å)0.494.034.160.534.034.084.150.564.034.064.140.594.034.064.14
Relaxor Ferroelectric-Normal Ferroelectric Solid Solutions
Relaxor ferroelectric-normal ferroelectric materials are disordered perovskite solid solutions on the B site between high dielectric constant relaxor ferroelectric materials and high Curie temperature normal ferroelectrics such as lead titanate (PT). These have achieved technological importance in single crystal form in piezoelectric transducers, actuators and sensors through increases in piezoelectric coefficients, d33, electromechanical coupling, k33, dielectric constants ∈33T/∈0 and saturation strains >1% while having lower losses and a lower modulus.
Relaxor perovskite materials have the formula Pb(BxB′(1−x))O3 where B is a low valence cation and B′ is a high valence cation. Two typical formula units are (1) Pb(B2+1/3B′5+2/3)O3, exemplified by Pb(Mg1/3Nb2/3)O3 (PMN) and Pb(Zn1/3Nb2/3)O3 (PZN) and (2) Pb(B3+1/2B′5+1/2)O3 exemplified by Pb(In3+1/2Nb5+1/2)O3 (PIN) and Pb(Yb3+1/2Nb5+1/2)O3 (PYN). First generation single crystals of binary PMN-PT solid solutions have been grown by the Bridgman method and offer high performance with ultra-high electromechanical coupling factors k33>0.9 and piezoelectric coefficients d33>1500 pC/N.
However, these materials are limited in temperature and acoustic power by TR-T, the rhombohedral to tetragonal phase transition temperature, which occurs at significantly lower temperatures than the Curie temperature TC. For many applications thermal stability is a requirement in terms of dielectric and piezoelectric property variations and thermal depolarization can result from post-fabrication processes.
In addition to the thermal environment, ferroelectric crystals used in electromechanical devices, such as high power ultrasonic transducers or actuators, are subjected to high electric fields, which necessitate that the crystals possess low dielectric/mechanical losses and relatively high coercive fields. The mechanical quality factors (Q) (inverse of the mechanical losses of the crystals) of PMN-PT and PZN-PT crystals are found to be less than 100, similar to “soft” PZT ceramics. The low mechanical Q limits single crystal PMN-PT to low frequency actuators or resonant power transducers that operate at low duty cycles. Furthermore, the coercive field (EC) of crystals, being only 2-3 kV/cm, restricts their use to low AC voltage applications or devices requiring a “biased” drive level.
Second generation ternary solid solutions among PIN, PMN and PT (PIMNT) and PYN, PMN and PT (PYMNT) have improved properties, but still much lower Curie and R-T transition temperatures than PZT as well as much lower mechanical Q's and coercivities. Thus, single crystal systems with high Curie and R-T transition temperatures are desired for enhanced temperature usage range, thermal stability and acoustic power.
The crystallization paths of these materials are as complex as the phase diagrams. Relaxor-PT ferroelectric single crystals are, by definition, solid solutions. For a simple binary solid solution phase diagram, the crystal composition that crystallizes first from any given melt composition will tend to be biased toward the higher melting compound. The farther apart the two melting points, the more the liquidus (temperature where the last solid phase melts on heating or the first solid phase appears on cooling) deviates from the solidus (temperature where the last liquid phase solidifies on cooling or the first liquid phase appears on heating) and therefore more segregation occurs. PMN-PT and PIMNT have been successfully grown up to 3″ in diameter by the Bridgman method. However the non-unity segregation coefficient KPT≈0.85 results in a gradient in the composition resulting from selective depletion of the more refractory PMN phase. Attempts have been made to alleviate this with zone leveling, but there is still a significant technological issue of non-uniformity of product.
Therefore commercial crystal growth of PMN-PT is initiated from a melt of composition that will produce the desired MPB monoclinic or multi-phase region in the main body of the crystal, but in fact the two ends are of different crystal structures with the PMN-rich bottom (first crystallized) being stable rhombohedral at room temperature, the middle being MPB with monoclinic structure coexisting with rhombohedral or tetragonal and the PT-rich top (last crystallized) being stable tetragonal at room temperature. A nominal 31% PT starting charge will vary in PT concentration from 26% at the seed to 40% at the end. Only the central MPB region with PT concentration 31-37% is used in device applications and the rhombohedral bottoms (26-30% PT) and tetragonal (38-40% PT) tops are cut off as scrap.
TABLE IIRoom temperature structures and lattice parameters of PMN relaxor ferroelectrics andtheir solid solutions with PT normal ferroelectrics. In the MPB region multiple phasesare present in the proportions shown with R = rhombohedral, M = Monoclinic,O = Orthorhombic and T = Tetragonal. The early data on rhombohedral phasesdoes often does not record (nr) the rhombohedral angle, but only the pseudo-cubic lattice constant a.RhombohedralMonoclinicTetragonalCompositionPT (%)Structurea (Å)α (°)a (Å)b (Å)c (Å)β (°)a (Å)c (Å)Ref.PMN0R4.0464nr[1]PMN-PT10R4.0386nr[1]PMN-PT20R4.0302nr[2]PMN-PT25R4.02489.915[3]PMN-PT30R4.01789.89[4]PMN-PT31R30%4.01789.894.0184.0074.02690.15[4]M70%PMN-PT33M75%4.0194.0064.03290.194.0054.046[4]T25%PMN-PT35T65%4.0184.0004.03590.124.0004.044[4]M/O35%PMN-PT37T80%3.9984.049[4]PMN-PT39T3.9944.047[4]PMN-PT39.5T3.9894.054[5]PMN-PT42T3.9844.054[5]PMN-PT44T3.9764.048[5]PMN-PT47T3.9784.056[5]PT100T3.90064.155[6][1] B. Dkhil, J. M. Kiat, G. Calvarin, G. Baldinozzi, S. B. Vakhrushev and E. Suard “Local and long range polar order in the relaxor-ferroelectric compounds PbMg1/3Nb2/3O3 and PbMg0.3Nb0.6Ti0.1O3” Phys. Rev. B 65 (2001) 024104.[2] H. W. King, S. H. Ferguson, D. F. Waechter and S. E. Prasad, “An X-ray Diffraction Study of PMN-PT Ceramics Near the Morphotropic Phase Boundary,” Proc. ICONS 2002 Inter. Conf. Sonar.[3] O. Noblanc, P Gaucher and G. Calvarin “Structural and dielectric studies of Pb(Mg1/3Nb2/3)O3— PbTiO3 ferroelectric solid solutions around the morphotropic boundary,” J. Appl. Phys. 79 (1996) 4291.[4] B. Noheda, D. E. Cox, G. Shirane, J. Gao and Z.-G. Ye, “Phase Diagram of the Ferroelectric Relaxor (1−x)PbMg1/3Nb2/3O3—xPbTiO3” Physical Review B 66 (2002) 054104.[5] J. C. Ho, K. S. Liu and I. N. Lin, “Study of Ferroelectricity in the PMN-PT System Near the Morphotropic Phase Boundary,” J. Mat. Sci 28 (1993) 4497.[6] S. A. Mabud and A. M. Glazer, Lattice Parameters and Birefringence in PbTiO3 Single Crystals,” J. Appl. Cryst. 12 (1979) 49.
High Temperature Solution Growth
High temperature solution (HTS) growth is useful for growth of “difficult” materials that for various reasons are not amenable to growth by conventional bulk techniques wherein the crystal is grown directly from the melted target compound. The list below covers a number of cases that are relevant to PZT.                Non-congruent melting materials (including peritectic melting) are those where the compound of interest does not crystallize directly from a liquid of the same composition at a local maximum (or minimum) on the melting curve. While lead titanate is congruently melting (FIG. 1); lead zirconate is not (FIG. 2) in part because of the refractory nature of zirconia (ZrO2—zirconium oxide) compounds. High melting point oxides are often outside the limits of bulk techniques because of limits on the use temperature of the crucible and other furnace materials or a high vapor pressure of a constituent.        Complex mixtures including solid solutions such as PZT and doped PZT have phase diagrams where the crystallizing compound can be very far off the melt composition.        Compounds with volatile constituents such as lead oxide may have to be equilibrated and grown at substantially lower temperatures than their melting point to be stable. It is preferred that the process temperature not exceed 900° C. This in turn limits the solubility of the crystal constituents.        
HTS growth gives the ability to vary growth conditions including temperature, chemical environment and atmosphere so that unstable crystal materials can be stabilized. The crystal growth system consisting of the solvent, solute, crucible, atmosphere and furnace should be stable in every way possible.
High Temperature Solution Growth of PZT
HTS growth of lead zirconate titanate (PZT-PbZrxTi1−xO3) crystals has been studied previously. The primary solvents have been so called “self-fluxes” with an excess of PbO7,8,9 and fluoride solvents10,11,12,13 KF, NaF and PbF2 alone or in mixtures comprising one or more halide compounds and PbO, Pb3(PO4)2 and/or B2O3. These studies include specific techniques of slow cooling, isothermal, localized cooling, solvent evaporation and top-seeded solution growth all of which require high solubility of PZT for success. The published experiments and results are summarized in Table III.
TABLE IIIGrowth parameters of HTS PZT crystal growth.xxSolventMethodT(start)T(end)Conc.(melt)(crystal)Ref.PbO (excess)Isothermal1100° C.ConstantVariousVariousZr rich [7]1200° C.1300° C.PbO (excess)Slow cool1170° C.950° C.VariousFIG. 3FIG. 3 [8]PbO (excess)Slow cool1170° C.950° C.0.150.40.06 [9]PbO—B2O3 (15:1)Isothermal967-Constant0.65-0.93 [9]1017° C.+PbTiO3PbO—PbF2Slow cool1200° C.800° C.0.15FIG. 4FIG. 4[10](50:50 start 60:40 end)KF—PbF2Slow cool1200° C.800° C.0.15FIG. 5FIG. 5[10](50:50 start 70:30 end)KF—PbF2Slow cool1150° C.950° C.0.10Various0-0.4[11]and 0.85(PbO)0.4(PbMoO4)0.6Slow coolVariousVariousVarious0.50.28[12](KF)0.4(PbF2)0.6Slow coolVariousVariousVarious0.50.26[12](NaF)1/3(PbF2)2/3Slow coolVariousVariousVarious0.50.4 [12](KF)0.30(PbF2)0.66Slow cool1115° C.800° C.0.150.50.45[13](Pb3(PO4)2)0.04[7] S. Fushimi and T. Ikeda, “Phase Equilibrium in the System PbO—TiO2—ZrO2.” J. Am. Ceram. Soc. 50: 119 (1967).[8] R. Clarke and R. W. Whatmore, “The Growth and Characterization of PbZrxTi1−xO3 Single Crystals,” J. Cryst. Growth 33: 29 (1976).[9] T. Hatanaka and H. Hasegawa, “Observation of Domain Structures in Tetragonal Pb(ZrxTi1−x)O3 Single Crystals by Chemical Etching Method,” Jpn. J. App. Phys. 31: 3245 (1992).[10] S. Fushimi and T. Ikeda, “Single Crystals of Lead Zirconate Titanate Solid Solutions,” Japan. J. Appl. Phys. 3: 171 (1964).[11] S. Fushimi and T. Ikeda, “Optical Study of Lead Zirconate-Titanate,” J. Phys. Soc. Japan 20: 2007 (1965).[12] K. Tsuzuki, et al., “Growth of Pb(Zr—Ti)O3 Single Crystal by Flux Method,” Japan. J. Appl. Phys. 7: 953 (1968).[13] K. Tsuzuki, et al., “The Growth of Ferroelectric Pb(ZrxTi1−x)O3 Single Crystals,” Japan. J. Appl. Phys. 12: 1500 (1973).
Various authors have also used a technique called flux growth, which differs from solution growth in that the constituents are not fully dissolved. In the flux method, crystal growth does not occur by nucleation and growth, but rather by transport of various nutrients between particulates that results in growth of larger crystallites at the expense of smaller ones. PbO—KF—PbCl2 fluxes used for this application have very high vapor pressures at the growth temperature and as much as ⅔ of the flux may evaporate during the growth run.
None of these results reach the level of being a viable process for PZT crystal growth.                The resultant crystals were at most a few millimeters on a side and typically thin plates because of the inherent limitations of these crystal growth techniques. Point seeded methods must grow out in three dimensions, which is a very time consuming process compared to common bulk crystallization methods such as Bridgman and Czochralski where there is a planar crystal growth front. Such point-seeded methods inherently produce crystals with well-developed facets. Such facets are the slowest growth direction and typically only advance by some sort of step propagation or dislocation model.        High temperatures >900° C. result in high evaporation of PbF2, PbO, KF, NaF and PbCl2 among other species. Evaporation of one or more species gives a continuously varying chemical environment and unstable growth conditions.        Slow cooling over a temperature range inherently gives a wide variety of growth conditions that are undoubtedly the source of compositional variations. Those authors who do not report compositional variations may only be reporting on a limited sample of crystals or an average value yielded by the characterization method (e.g., x-ray powder diffraction).        None of the authors have measured the solubility of PZ and PT, or alternatively ZrO2 and TiO2, under the growth conditions. Therefore it is unknown at what saturation (liquidus) temperature any given melt composition may actually produce crystals. In fact, it is entirely possible that in some instances not all the zirconia or PZ is dissolved in the melt and any crystal growth may be occurring by the flux method rather than true HTS growth.        There are a diversity of Zr/Ti distribution coefficients seen both above and below unity depending on the choice of solvent, ZrO2 fraction x relative to TiO2 in the melt and other factors that are not properly recorded including actual growth temperature.        In some cases, phase separation into Zr-rich and Ti-rich phases is seen. One group observed a positive heat of mixing for PZT in a 3Na2O-4MoO4 solution. Such phase separation is not seen in solid phase sintering.        
Therefore an inventive method is required that can sustain a uniform MPB composition and produce a planar crystal growth front to grow large crystals.
Freezing Point Depression (Cryoscopy)
Cryoscopy is the study of the properties of a multi-component solution by the depression of the freezing point of one or more components. Typically it is used to measure the molecular weight or degree of dissociation of a small quantity of one component dissolved in a bulk liquid of another component.
If two melt constituents C and D in a binary melt do not form a solid solution (at least not to a significant extent), adding C to D in the liquid lowers the freezing point of a solid (presumably a crystal) of pure C because of the entropy of mixing in the C-D liquid solution. If the assumption is made that this is an ideal solution and the attractive forces between like and unlike atoms are the same, a derivation may be made from Raoult's Law and the Clausius-Clapeyron equation that yields
                              ln          ⁡                      (                          X              C                        )                          =                              -                                          Δ                ⁢                                                                  ⁢                                  H                  f                                            nR                                ⁢                      (                                          1                T                            -                              1                                  T                  M                                                      )                                              (        1        )            where XC is the mole fraction of C, ΔHf is the enthalpy of fusion of C, n is the Van 't Hoff factor, R is the gas constant, TM is the melting temperature of a pure C melt and T is the liquidus temperature of the diluted solution in K where the first appearance of a solid phase occurs.
The Van 't Hoff factor n is nominally the number of particles into which D dissolves in an ideal solution of C that are distinct from the particles into which C melts in solution. In a non-ideal solution n may take on a wider range of values depending on whether the atoms or complexes of D are attracted (smaller n) or repelled (greater n) by one another. n of D can be different for different C components depending on the nature of the liquid.
Liquid Phase Epitaxy
Epitaxy is when a crystal of one material is grown on top of and in registry with another material. Liquid phase epitaxy (LPE) is depicted atomistically in FIG. 6 and pictorially in FIG. 7. Other HTS techniques such as slow cooling, localized cooling, solvent evaporation and top-seeded solution growth require high solute concentrations and typically involve cooling over a wide temperature range such that the thermodynamic conditions vary significantly with the common result that the crystal composition also varies. LPE is unique in that it is a near equilibrium high temperature solution growth technique undertaken at near constant growth conditions from a relatively dilute melt. Accordingly, high crystal quality at constant target stoichiometry can be achieved with the proper match between film and substrate.
To grow quality crystals, the film and substrate must have an acceptable match in structure, lattice parameter and coefficient of thermal expansion. Congruently melting substrate crystals growable by some bulk method can be matched up with non-congruent films that must be grown by HTS techniques to produce film/substrate combinations with effective composite properties. The substrate must be of good crystal quality as any defects will propagate into the film. Compared to point-seeded methods, LPE has a high volumetric growth rate because the crystal only needs to expand in one dimension with a planar growth front. Compared to vapor phase methods, there is a much higher flow of nutrient, so thicker films are practical at higher growth rates and, in fact, for a good enough coefficient of thermal expansion match, film thicknesses can be achieved that are of similar magnitude to the substrate thickness, effectively growing bulk crystal plates that can be made free-standing by removing the substrate through lapping and polishing. LPE is best conducted from a more dilute melt so homogeneous nucleation of crystallites is avoided and crystal growth can be controlled at a variety of undercoolings. LPE is also best done at the lowest possible temperature to achieve the desired phase as close as possible to equilibrium. In particular, anti-site defects are avoided at lower growth temperatures. The solvent must wet the substrate for good growth.
LPE has reached its zenith to date in the HTS growth of magnetic garnets on Czochralski-grown non-magnetic garnet substrates for thin-film magnetic bubble and thick-film magnetooptic applications. LPE has been shown to be a practical high throughput technique for the growth of thick film garnet Faraday rotator materials (˜500 μm films) with only ˜1 mol % of the limiting rare earth oxide. The garnet system is similar to perovskites in that the materials are adaptable because the crystal structure is defined by a network of oxygen atoms.